The reweighted Landweber scheme for the extrapolation of band-limited signals

Abstract

The extrapolation of a band-limited signal is in terms of a finite known segment of it in the time interval [−T,T] for T > 0 to determine the unknown part of the signal. Extrapolation in the frequency domain is represented by an integral equation and then discretized as a linear system. If T is small, the theoretical ill-posedness of the extrapolation leads to the linear system having ill-posedness because the condition number of the coefficient matrix is large. The condition number of a matrix equals the maximum singular value of the matrix divided by the minimum singular value. Owing to the large condition number, the solution contains large error, relative to the true solution. We use a reweighting method to improve the condition number for the extrapolation of band-limited signal simulations and propose a reweighted Landweber scheme. Simulations validate the proposed method. Effective reconstructions are obtained from the same number of samples in an appropriately small time interval [−T,T].